public static void Multiply(uint[] x, uint[] y, uint[] z)
{
var tt = Nat256.CreateExt();
Nat256.Mul(x, y, tt);
Reduce(tt, z);
}
public static void Mul(uint[] x, uint[] y, uint[] zz)
{
Nat256.Mul(x, y, zz);
Nat256.Mul(x, 8, y, 8, zz, 16);
uint num = Nat256.AddToEachOther(zz, 8, zz, 16);
uint cIn = num + Nat256.AddTo(zz, 0, zz, 8, 0u);
num += Nat256.AddTo(zz, 24, zz, 16, cIn);
uint[] array = Nat256.Create();
uint[] array2 = Nat256.Create();
bool flag = Nat256.Diff(x, 8, x, 0, array, 0) != Nat256.Diff(y, 8, y, 0, array2, 0);
uint[] array3 = Nat256.CreateExt();
Nat256.Mul(array, array2, array3);
num = (uint)((int)num + ((!flag) ? Nat.SubFrom(16, array3, 0, zz, 8) : ((int)Nat.AddTo(16, array3, 0, zz, 8))));
Nat.AddWordAt(32, num, zz, 24);
}
public static void Mul(uint[] x, uint[] y, uint[] zz)
{
Nat256.Mul(x, y, zz);
Nat256.Mul(x, 8, y, 8, zz, 16);
uint c24 = Nat256.AddToEachOther(zz, 8, zz, 16);
uint c16 = c24 + Nat256.AddTo(zz, 0, zz, 8, 0);
c24 += Nat256.AddTo(zz, 24, zz, 16, c16);
uint[] dx = Nat256.Create(), dy = Nat256.Create();
bool neg = Nat256.Diff(x, 8, x, 0, dx, 0) != Nat256.Diff(y, 8, y, 0, dy, 0);
uint[] tt = Nat256.CreateExt();
Nat256.Mul(dx, dy, tt);
c24 += neg ? Nat.AddTo(16, tt, 0, zz, 8) : (uint)Nat.SubFrom(16, tt, 0, zz, 8);
Nat.AddWordAt(32, c24, zz, 24);
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(Twice());
}
ECCurve curve = this.Curve;
SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord;
SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord;
SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat256.CreateExt();
uint[] t2 = Nat256.Create();
uint[] t3 = Nat256.Create();
uint[] t4 = Nat256.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP256K1Field.Square(Z1.x, S2);
U2 = t2;
SecP256K1Field.Multiply(S2, X2.x, U2);
SecP256K1Field.Multiply(S2, Z1.x, S2);
SecP256K1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP256K1Field.Square(Z2.x, S1);
U1 = tt1;
SecP256K1Field.Multiply(S1, X1.x, U1);
SecP256K1Field.Multiply(S1, Z2.x, S1);
SecP256K1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
SecP256K1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP256K1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.IsZero(H))
{
if (Nat256.IsZero(R))
{
// this == b, i.e. this must be doubled
return(this.Twice());
}
// this == -b, i.e. the result is the point at infinity
return(curve.Infinity);
}
uint[] HSquared = t3;
SecP256K1Field.Square(H, HSquared);
uint[] G = Nat256.Create();
SecP256K1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP256K1Field.Multiply(HSquared, U1, V);
SecP256K1Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
SecP256K1Field.Reduce32(c, G);
SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4);
SecP256K1Field.Square(R, X3.x);
SecP256K1Field.Subtract(X3.x, G, X3.x);
SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G);
SecP256K1Field.Subtract(V, X3.x, Y3.x);
SecP256K1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP256K1Field.Reduce(tt1, Y3.x);
SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H);
if (!Z1IsOne)
{
SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP256K1Point(curve, X3, Y3, zs, IsCompressed));
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] array = Nat256.CreateExt();
Nat256.Mul(x, y, array);
Reduce(array, z);
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(Twice());
}
ECCurve curve = Curve;
Curve25519FieldElement curve25519FieldElement = (Curve25519FieldElement)base.RawXCoord;
Curve25519FieldElement curve25519FieldElement2 = (Curve25519FieldElement)base.RawYCoord;
Curve25519FieldElement curve25519FieldElement3 = (Curve25519FieldElement)base.RawZCoords[0];
Curve25519FieldElement curve25519FieldElement4 = (Curve25519FieldElement)b.RawXCoord;
Curve25519FieldElement curve25519FieldElement5 = (Curve25519FieldElement)b.RawYCoord;
Curve25519FieldElement curve25519FieldElement6 = (Curve25519FieldElement)b.RawZCoords[0];
uint[] array = Nat256.CreateExt();
uint[] array2 = Nat256.Create();
uint[] array3 = Nat256.Create();
uint[] array4 = Nat256.Create();
bool isOne = curve25519FieldElement3.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = curve25519FieldElement4.x;
array6 = curve25519FieldElement5.x;
}
else
{
array6 = array3;
Curve25519Field.Square(curve25519FieldElement3.x, array6);
array5 = array2;
Curve25519Field.Multiply(array6, curve25519FieldElement4.x, array5);
Curve25519Field.Multiply(array6, curve25519FieldElement3.x, array6);
Curve25519Field.Multiply(array6, curve25519FieldElement5.x, array6);
}
bool isOne2 = curve25519FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = curve25519FieldElement.x;
array8 = curve25519FieldElement2.x;
}
else
{
array8 = array4;
Curve25519Field.Square(curve25519FieldElement6.x, array8);
array7 = array;
Curve25519Field.Multiply(array8, curve25519FieldElement.x, array7);
Curve25519Field.Multiply(array8, curve25519FieldElement6.x, array8);
Curve25519Field.Multiply(array8, curve25519FieldElement2.x, array8);
}
uint[] array9 = Nat256.Create();
Curve25519Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
Curve25519Field.Subtract(array8, array6, array10);
if (Nat256.IsZero(array9))
{
if (Nat256.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = Nat256.Create();
Curve25519Field.Square(array9, array11);
uint[] array12 = Nat256.Create();
Curve25519Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
Curve25519Field.Multiply(array11, array7, array13);
Curve25519Field.Negate(array12, array12);
Nat256.Mul(array8, array12, array);
uint x = Nat256.AddBothTo(array13, array13, array12);
Curve25519Field.Reduce27(x, array12);
Curve25519FieldElement curve25519FieldElement7 = new Curve25519FieldElement(array4);
Curve25519Field.Square(array10, curve25519FieldElement7.x);
Curve25519Field.Subtract(curve25519FieldElement7.x, array12, curve25519FieldElement7.x);
Curve25519FieldElement curve25519FieldElement8 = new Curve25519FieldElement(array12);
Curve25519Field.Subtract(array13, curve25519FieldElement7.x, curve25519FieldElement8.x);
Curve25519Field.MultiplyAddToExt(curve25519FieldElement8.x, array10, array);
Curve25519Field.Reduce(array, curve25519FieldElement8.x);
Curve25519FieldElement curve25519FieldElement9 = new Curve25519FieldElement(array9);
if (!isOne)
{
Curve25519Field.Multiply(curve25519FieldElement9.x, curve25519FieldElement3.x, curve25519FieldElement9.x);
}
if (!isOne2)
{
Curve25519Field.Multiply(curve25519FieldElement9.x, curve25519FieldElement6.x, curve25519FieldElement9.x);
}
uint[] zSquared = (!isOne || !isOne2) ? null : array11;
Curve25519FieldElement curve25519FieldElement10 = CalculateJacobianModifiedW(curve25519FieldElement9, zSquared);
ECFieldElement[] zs = new ECFieldElement[2]
{
curve25519FieldElement9,
curve25519FieldElement10
};
return(new Curve25519Point(curve, curve25519FieldElement7, curve25519FieldElement8, zs, base.IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(Twice());
}
ECCurve curve = Curve;
SecP256R1FieldElement secP256R1FieldElement = (SecP256R1FieldElement)base.RawXCoord;
SecP256R1FieldElement secP256R1FieldElement2 = (SecP256R1FieldElement)base.RawYCoord;
SecP256R1FieldElement secP256R1FieldElement3 = (SecP256R1FieldElement)b.RawXCoord;
SecP256R1FieldElement secP256R1FieldElement4 = (SecP256R1FieldElement)b.RawYCoord;
SecP256R1FieldElement secP256R1FieldElement5 = (SecP256R1FieldElement)base.RawZCoords[0];
SecP256R1FieldElement secP256R1FieldElement6 = (SecP256R1FieldElement)b.RawZCoords[0];
uint[] array = Nat256.CreateExt();
uint[] array2 = Nat256.Create();
uint[] array3 = Nat256.Create();
uint[] array4 = Nat256.Create();
bool isOne = secP256R1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP256R1FieldElement3.x;
array6 = secP256R1FieldElement4.x;
}
else
{
array6 = array3;
SecP256R1Field.Square(secP256R1FieldElement5.x, array6);
array5 = array2;
SecP256R1Field.Multiply(array6, secP256R1FieldElement3.x, array5);
SecP256R1Field.Multiply(array6, secP256R1FieldElement5.x, array6);
SecP256R1Field.Multiply(array6, secP256R1FieldElement4.x, array6);
}
bool isOne2 = secP256R1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP256R1FieldElement.x;
array8 = secP256R1FieldElement2.x;
}
else
{
array8 = array4;
SecP256R1Field.Square(secP256R1FieldElement6.x, array8);
array7 = array;
SecP256R1Field.Multiply(array8, secP256R1FieldElement.x, array7);
SecP256R1Field.Multiply(array8, secP256R1FieldElement6.x, array8);
SecP256R1Field.Multiply(array8, secP256R1FieldElement2.x, array8);
}
uint[] array9 = Nat256.Create();
SecP256R1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP256R1Field.Subtract(array8, array6, array10);
if (Nat256.IsZero(array9))
{
if (Nat256.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP256R1Field.Square(array9, array11);
uint[] array12 = Nat256.Create();
SecP256R1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP256R1Field.Multiply(array11, array7, array13);
SecP256R1Field.Negate(array12, array12);
Nat256.Mul(array8, array12, array);
uint x = Nat256.AddBothTo(array13, array13, array12);
SecP256R1Field.Reduce32(x, array12);
SecP256R1FieldElement secP256R1FieldElement7 = new SecP256R1FieldElement(array4);
SecP256R1Field.Square(array10, secP256R1FieldElement7.x);
SecP256R1Field.Subtract(secP256R1FieldElement7.x, array12, secP256R1FieldElement7.x);
SecP256R1FieldElement secP256R1FieldElement8 = new SecP256R1FieldElement(array12);
SecP256R1Field.Subtract(array13, secP256R1FieldElement7.x, secP256R1FieldElement8.x);
SecP256R1Field.MultiplyAddToExt(secP256R1FieldElement8.x, array10, array);
SecP256R1Field.Reduce(array, secP256R1FieldElement8.x);
SecP256R1FieldElement secP256R1FieldElement9 = new SecP256R1FieldElement(array9);
if (!isOne)
{
SecP256R1Field.Multiply(secP256R1FieldElement9.x, secP256R1FieldElement5.x, secP256R1FieldElement9.x);
}
if (!isOne2)
{
SecP256R1Field.Multiply(secP256R1FieldElement9.x, secP256R1FieldElement6.x, secP256R1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1]
{
secP256R1FieldElement9
};
return(new SecP256R1Point(curve, secP256R1FieldElement7, secP256R1FieldElement8, zs, base.IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(Twice());
}
ECCurve curve = this.Curve;
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0];
Curve25519FieldElement X2 = (Curve25519FieldElement)b.RawXCoord, Y2 = (Curve25519FieldElement)b.RawYCoord,
Z2 = (Curve25519FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat256.CreateExt();
uint[] t2 = Nat256.Create();
uint[] t3 = Nat256.Create();
uint[] t4 = Nat256.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
Curve25519Field.Square(Z1.x, S2);
U2 = t2;
Curve25519Field.Multiply(S2, X2.x, U2);
Curve25519Field.Multiply(S2, Z1.x, S2);
Curve25519Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
Curve25519Field.Square(Z2.x, S1);
U1 = tt1;
Curve25519Field.Multiply(S1, X1.x, U1);
Curve25519Field.Multiply(S1, Z2.x, S1);
Curve25519Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
Curve25519Field.Subtract(U1, U2, H);
uint[] R = t2;
Curve25519Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.IsZero(H))
{
if (Nat256.IsZero(R))
{
// this == b, i.e. this must be doubled
return(this.Twice());
}
// this == -b, i.e. the result is the point at infinity
return(curve.Infinity);
}
uint[] HSquared = Nat256.Create();
Curve25519Field.Square(H, HSquared);
uint[] G = Nat256.Create();
Curve25519Field.Multiply(HSquared, H, G);
uint[] V = t3;
Curve25519Field.Multiply(HSquared, U1, V);
Curve25519Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
Curve25519Field.Reduce27(c, G);
Curve25519FieldElement X3 = new Curve25519FieldElement(t4);
Curve25519Field.Square(R, X3.x);
Curve25519Field.Subtract(X3.x, G, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(G);
Curve25519Field.Subtract(V, X3.x, Y3.x);
Curve25519Field.MultiplyAddToExt(Y3.x, R, tt1);
Curve25519Field.Reduce(tt1, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(H);
if (!Z1IsOne)
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
Curve25519Field.Multiply(Z3.x, Z2.x, Z3.x);
}
uint[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null;
// TODO If the result will only be used in a subsequent addition, we don't need W3
Curve25519FieldElement W3 = CalculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared);
ECFieldElement[] zs = new ECFieldElement[] { Z3, W3 };
return(new Curve25519Point(curve, X3, Y3, zs, IsCompressed));
}
public override ECPoint Add(ECPoint b)
{
uint[] numArray5;
uint[] numArray6;
uint[] numArray7;
uint[] numArray8;
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
if (this == b)
{
return(this.Twice());
}
ECCurve curve = this.Curve;
Curve25519FieldElement rawXCoord = (Curve25519FieldElement)base.RawXCoord;
Curve25519FieldElement rawYCoord = (Curve25519FieldElement)base.RawYCoord;
Curve25519FieldElement element3 = (Curve25519FieldElement)base.RawZCoords[0];
Curve25519FieldElement element4 = (Curve25519FieldElement)b.RawXCoord;
Curve25519FieldElement element5 = (Curve25519FieldElement)b.RawYCoord;
Curve25519FieldElement element6 = (Curve25519FieldElement)b.RawZCoords[0];
uint[] zz = Nat256.CreateExt();
uint[] numArray2 = Nat256.Create();
uint[] numArray3 = Nat256.Create();
uint[] x = Nat256.Create();
bool isOne = element3.IsOne;
if (isOne)
{
numArray5 = element4.x;
numArray6 = element5.x;
}
else
{
numArray6 = numArray3;
Curve25519Field.Square(element3.x, numArray6);
numArray5 = numArray2;
Curve25519Field.Multiply(numArray6, element4.x, numArray5);
Curve25519Field.Multiply(numArray6, element3.x, numArray6);
Curve25519Field.Multiply(numArray6, element5.x, numArray6);
}
bool flag2 = element6.IsOne;
if (flag2)
{
numArray7 = rawXCoord.x;
numArray8 = rawYCoord.x;
}
else
{
numArray8 = x;
Curve25519Field.Square(element6.x, numArray8);
numArray7 = zz;
Curve25519Field.Multiply(numArray8, rawXCoord.x, numArray7);
Curve25519Field.Multiply(numArray8, element6.x, numArray8);
Curve25519Field.Multiply(numArray8, rawYCoord.x, numArray8);
}
uint[] z = Nat256.Create();
Curve25519Field.Subtract(numArray7, numArray5, z);
uint[] numArray10 = numArray2;
Curve25519Field.Subtract(numArray8, numArray6, numArray10);
if (Nat256.IsZero(z))
{
if (Nat256.IsZero(numArray10))
{
return(this.Twice());
}
return(curve.Infinity);
}
uint[] numArray11 = Nat256.Create();
Curve25519Field.Square(z, numArray11);
uint[] numArray12 = Nat256.Create();
Curve25519Field.Multiply(numArray11, z, numArray12);
uint[] numArray13 = numArray3;
Curve25519Field.Multiply(numArray11, numArray7, numArray13);
Curve25519Field.Negate(numArray12, numArray12);
Nat256.Mul(numArray8, numArray12, zz);
Curve25519Field.Reduce27(Nat256.AddBothTo(numArray13, numArray13, numArray12), numArray12);
Curve25519FieldElement element7 = new Curve25519FieldElement(x);
Curve25519Field.Square(numArray10, element7.x);
Curve25519Field.Subtract(element7.x, numArray12, element7.x);
Curve25519FieldElement y = new Curve25519FieldElement(numArray12);
Curve25519Field.Subtract(numArray13, element7.x, y.x);
Curve25519Field.MultiplyAddToExt(y.x, numArray10, zz);
Curve25519Field.Reduce(zz, y.x);
Curve25519FieldElement element9 = new Curve25519FieldElement(z);
if (!isOne)
{
Curve25519Field.Multiply(element9.x, element3.x, element9.x);
}
if (!flag2)
{
Curve25519Field.Multiply(element9.x, element6.x, element9.x);
}
uint[] zSquared = (!isOne || !flag2) ? null : numArray11;
Curve25519FieldElement element10 = this.CalculateJacobianModifiedW(element9, zSquared);
ECFieldElement[] zs = new ECFieldElement[] { element9, element10 };
return(new Curve25519Point(curve, element7, y, zs, base.IsCompressed));
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] zz = Nat256.CreateExt();
Nat256.Mul(x, y, zz);
Reduce(zz, z);
}